Complex K-theory of dual Hitchin systems

Geometry, Symmetry and Physics
Event time: 
Monday, October 25, 2021 - 4:30pm
Michael Groechenig
Speaker affiliation: 
University of Toronto
Event description: 

Abstract: Let G and G’ be Langlands dual reductive groups (e.g. SL(n) and PGL(n)). According to a theorem by Donagi-Pantev, the generic fibres of the moduli spaces of G-Higgs bundles and G’-Higgs bundles are dual abelian varieties and are therefore derived equivalent. It is an interesting open problem to prove existence of a derived equivalence over the full Hitchin base. I will report on joint work in progress with Shiyu Shen, in which we construct a K-theoretic shadow thereof: natural equivalences between complex K-theory spectra for certain moduli spaces of Higgs bundles (in type A).

Zoom link:, contact the organizers (Gurbir Dhillon and Junliang Shen) for the passcode.